"Assent to a proposition or affirmation, or the acceptance of a fact, opinion, or assertion as real or true, without immediate personal knowledge; reliance upon word or testimony; partial or full assurance without positive knowledge or absolute certainty; persuasion; conviction; confidence; as, belief of a witness; the belief of our senses." --Webster's Revised Unabridged Dictionary (1913)
From this it follows that belief can only occur where acceptance is not compelled, for if acceptance is compelled, then belief is not required to accept that thing. Belief is thus the acceptance of some thing as being provisionally true where:
Alternatively an agent can be attributed a belief in X when it acts[1] as if X is true. This sense of the word seems to be more common (in North America) and in the philosophical literature I've read. --DavidLucifer
[1] Assuming that the act is sincere, that is, without deception or sarcasm.
See also: acceptance, faith, trust, truth, truth value, weyken Discussion-Lexicon-Belief-2003-09-03